Finite Group Databasebeta

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C52⋊C3×D29⋊C7 #44478550

order30450
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C5

Aliases

direct productC52⋊C3×D29⋊C7
unambiguous semidirect productD29⋊(C7×C52⋊C3)
unambiguous semidirect product(C29⋊C7)⋊(C2×C52⋊C3)
unambiguous semidirect product(D29×C52⋊C3)⋊C7
unambiguous semidirect product(C52×D29⋊C7)⋊C3

Splittings

Fitting, socle, derived, HallC52×C29 ⋊ C2×C3×C7
HallC52⋊C3×C29⋊C7 ⋊ C2
HallC52×D29⋊C7 ⋊ C3
HallC52×C29⋊C7 ⋊ C2×C3
HallD29×C52⋊C3 ⋊ C7
HallC29×C52⋊C3 ⋊ C2×C7
HallC52×D29 ⋊ C3×C7
HallC29⋊C7 ⋊ C2×C52⋊C3
HallD29 ⋊ C7×C52⋊C3
SylowC29 ⋊ C2×C7×C52⋊C3
SylowC52 ⋊ C3×D29⋊C7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C29C2×C3×C7
LCSG ▷ C52×C29
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 435

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 34);